Each year, more than 5 million Americans are diagnosed with cardiac valve disease. Among the valvular diseases, aortic valve stenosis (AVS) is the most common. With the aging population, the prevalence of AVS is expected to rise. Timing of intervention for AVS is largely based on the severity of stenosis and the presence of symptoms. Therefore, accurate assessment of the functional severity of stenosis is important when making clinical decisions regarding intervention. Currently, the most common non-invasive method for the assessment of AVS severity is Transthoracic Doppler echocardiography (TTE). However, many patients may have suboptimal evaluation with echocardiography due to poor acoustic windows, heavy calcification of the aortic valve, or significant flow acceleration in the left ventricular outflow tract which may obscure assessment of the aortic valve. For such patients, MRI-based 2D flow imaging (MRI-2DF), which is not impacted by acoustic windows, provides a viable alternative. MRI-2DF methods, however, are only sensitive to one directional component of the velocity vector; therefore, any misalignment of the velocity encoding direction with respect to the blood flow direction results in underestimation of the flow and velocity and, i turn, potential misclassification of disease severity. PC-MRI-based 4D flow imaging (MRI-4DF), with its volumetric spatial coverage and ability to encode all directions of the velocity, circumvents the shortcoming associated with TTE and MRI-2DF and thus can improve evaluation of AVS severity. The promise of MRI-4DF, however, is undone by prohibitively long scan times, which can be over 30 min. Despite recent efforts in utilizing parallel imaging, non-Cartesian trajectories, and compressive sensing (CS) inspired image recovery, MRI-4DF remains a research tool that is in need of further development to find clinical application. The goal of this work is to enable and demonstrate the feasibility of single breath-hold MRI-4DF in a small cohort of patients with AVS. In Specific Aim 1, we propose a novel technique, called Reconstructing Velocity Encoded MRI with Approximate message passing aLgorithms (ReVEAL), to reduce the acquisition time for MRI-4DF to a single breath-hold. In contrast to the existing CS techniques that utilize the underlying image sparsity, ReVEAL directly models the strong physical relationships inherent in the PC-MRI data. In particular, the proposed Bayesian approach capitalizes on the relationships in both magnitude and phase among the several velocity encodings. To solve the resulting Bayesian inference problem, an iterative image recovery method using message passing on a factor graph is proposed, yielding a fast algorithm with auto-tuning of all free parameters. In Specific Aim 2, we will use MRI-4DF data from a mechanical flow phantom and thirty AVS patients to validate the proposed approach. Preliminary results show that ReVEAL can accelerate MRI-2DF by a factor of 12; higher accelerations are expected for MRI-4DF due to added redundancy. This development will lead to more accurate characterization of cardiac valve disease than is possible with existing clinical methods.